Solving linear equations over finitely generated abelian groups

René Hartung

Solving linear equations over finitely generated abelian groups

Group Theory 2010-07-16 v1

Authors: René Hartung

Abstract

We discuss various methods and their effectiveness for solving linear equations over finitely generated abelian groups. More precisely, if $\varphi\colon G\to H$ is a homomorphism of finitely generated abelian groups and $b\in H$ , we discuss various algorithms for checking whether $b\in \im\varphi$ holds and if so, for computing a pre-image of $b$ in $G$ together with the kernel of $\varphi$ .

Keywords

abelian groups group theory finite group theory

Cite

@article{arxiv.1007.2477,
  title  = {Solving linear equations over finitely generated abelian groups},
  author = {René Hartung},
  journal= {arXiv preprint arXiv:1007.2477},
  year   = {2010}
}

Comments

12 pages; draft

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